wckronholm | 10 years ago | on: Vector Space Systems aims to launch satellites by the hundreds
It should be easy for them to get the satellites up: just point them up and multiply by the right scalar.
wckronholm's comments
wckronholm | 10 years ago | on: The Basics of Web Application Security
A bit of a bummer that http://evil.martinfowler.com/ resulted in Server Not Found.
wckronholm | 10 years ago | on: Essential Copying and Pasting from Stack Overflow
It's the only book I've ever written.
wckronholm | 10 years ago | on: Why 5 x 3 = 5 and 5 and 5 Was Marked Wrong
If the author of this article instead references the definition of multiplication of natural numbers on wikipedia [1], then the student is correct since $a \times b = a + a + \dots + a$ with that definition.
Without access to this particular teacher's curriculum materials, it's not possible to know for sure what definition is being referenced by the "repeated addition strategy". I'm inclined to assume the teacher knows what they're doing and has graded the work appropriately.
There are many comments on this thread about multiplication being commutative by definition, but this is not quite correct. Following the same definition of multiplication I cited above, it is a theorem that $a \times b = b \times a$. When I teach Abstract Thinking (a sort of introduction to proof writing course for mathematics students), I have the students write proofs for this property of multiplication of natural numbers, and the other familiar properties (cancellation, distribution, etc.). If anyone is interested, I've broken the steps out into worksheets that I give to my students, and you can see them at the link below. [2] [pdf] (Multiplication of natural numbers is section 5.5.)
[1] https://en.wikipedia.org/wiki/Natural_number#Multiplication [2] [pdf] http://billkronholm.com/wp-content/uploads/2015/10/MATH280.p...
wckronholm | 11 years ago | on: The Sierpinski triangle page to end most Sierpinski triangle pages
I don't know. What If I took that page and divided it into <div>'s, removed the middle one, and replaced the others with copies of the original page? Then, I could take each of those <div>'s, break them into pieces, remove the middle one, and replace the others with copies of the original page. Then...
wckronholm | 11 years ago | on: Show HN: Search free-to-use (CC0) images by keyword, color, attribute
Why does the keyword search drop the final character if it is an 's'? For example, when I search for 'dress' the message I receive is 'Showing 0 images tagged dres'
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